Essentials of Vehicle Dynamics

Appendix 5

Lagrange Equations

Consider a mechanical system with n generalized coordinates q_i, i=1, …, n. Assume that generalized nonconservative forces Q_i exist, meaning that these forces (or moments) cannot be expressed as a gradient −∇U of a potential function U(q_i) (i.e., of the potential energy), and do not depend on the generalized coordinates q_i and their time derivatives. The total transfer of energy is given by the following function:

$L^{*}=T-U+\sum _i{q}_i\cdot Q_i$ (A5.1)

(A5.1)

with kinetic energy T, potential energy U, and work being carried out using the nonconservative forces Q_i. The first part of the right-hand side in Eq. (A5.1) is usually referred ...